Film and television
Encouraged by his father, Braun began to take acting classes at a very young age.
Braun is 6 ft 7 in (2.01 m). He has said his height has cost him parts and that he occasionally tried to present himself as shorter early in his career.
He made his film debut in Sky High. He had roles in the Disney Channel Original Movies Minutemen (2008) and Princess Protection Program (2009). He played the regular role of Cameron on the ABC Family show 10 Things I Hate About You, until it was cancelled with its final episode airing on May 24, 2010. He appeared in The Secret Life of the American Teenager and portrayed the character Cole Waters on the web series The LXD. In 2011, he played Lloyd Taylor in Disney's theatrical release Prom, and Billy Ray in Kevin Smith's Red State. The following year, he had a supporting role in the coming-of-age film The Perks of Being a Wallflower (2012).
In 2015, he was featured on two tracks of the Phantoms' debut EP, Broken Halo. He provided vocals on the title track and on "Voyeur". He also co-starred in both Date and Switch (2014) and How to Be Single (2016). He played Derrek in the A24 drama film Zola (2021), which was directed by Janicza Bravo and written by Jeremy O. Harris. The film received positive reviews.
In 2018, Braun became a member of the main cast of the HBO drama series Succession, playing Gregory Hirsch. For his performance in the show, Braun received critical acclaim and was nominated three times—in 2020, 2022, and 2023—for a Primetime Emmy Award for Outstanding Supporting Actor in a Drama Series.
On July 29, 2020, Braun released the music video for his single "Antibodies (Do You Have The)". He stated that the song was made in partnership with Partners In Health and the COPE Program to encourage listeners to donate in support of those most at risk from the pandemic.
In 2022, he appeared in the IFC mockumentary series Documentary Now! episode "Soldier of Illusion, Parts 1 & 2", directed by Alex Buono and Rhys Thomas. The installment parodied the films of Werner Herzog and was written by John Mulaney.
Braun starred in the Susanna Fogel drama Cat Person (2023), which premiered at the 2023 Sundance Film Festival. The film is based on the 2017 short story featured in The New Yorker, which was released amid the MeToo movement. Braun then appeared in the fantasy film Dream Scenario, directed by Kristoffer Borgli. He was cast as both filmmaker Jim Henson and entertainer Andy Kaufman for the 2024 biographical dramedy Saturday Night and appeared in the 2026 thriller The Sheep Detectives, based on the novel Three Bags Full.